Constraints for attaching planar object to multiple poles
I'm not sure about your constraints, but this might be a solution?


Hook each plane corner to an empty (select the vertex and ctrlH > Hook to New Object).
Create your 4 poles (here I've created one cylinder pole).
Parent each empty to your pole.
Move your pole, the corner will follow.
Give your poles some Limit Location constraints if you don't want them to move on the Z axis or if you want to limit them on a certain X or Y area.